My name is Valentin Haberl and I am a PhD student working in set theory and set-theoretic topology at TUW. My advisor is Lyubomyr Zdomskyy. I am a member of the research group FB8 Set Theory and work as a project assistant at TUW in the framework of the FWF project I5930 with the title “Set-theoretic aspects of topological selections”. This project is a collaboration between my advisor and Piotr Szewczak from the Cardinal Stefan Wyszyński University in Warsaw.
Research interests
My research is about the investigation of possible cardinalities of spaces satisfying selection principles in forcing extensions. This includes studying combinatorial covering properties in standard models of set theory as well as creating new models with forcing to obtain consistency results.
I am especially interested in the following subjects:
- Selection principles (combinatorial covering properties)
- Set theory
- Forcing theory
- Cardinal characteristics
- Set theory of the real line
- Consistency results in general topology
- Large cardinals
Education
I studied the Mathematics bachelor’s and master’s programs at Karl-Franzens-University of Graz. My master’s thesis has the title “Tukey order on hyperspaces of compact subspaces and covering properties” and was written under the supervision of Lyubomyr Zdomskyy (TUW). My bachelor’s thesis, “The fixed-point theorems of Banach and Brouwer with application in the Minimax-theorem” (original german title: “Die Fixpunktsätze von Banach und Brouwer mit Anwendung im Minimax-Satz”), was written in German under the supervision of Christoph Aistleitner (TU Graz).